Question

An unknown solution x has a molar mass of 17n molarity of 15.2m and density of 0.8980g/ml calculate the mole fraction of x

Answer 1

Given:

Molar mass = 17 gm

Molarity = 15.2 m

Density = 0.898 g/ml

To Find:

Mole Fraction of x

Calculation:

- We know the formula:

Molarity = (10 × d × wt %) / M.wt

⇒ 15.2 = (10 × 0.898 × wt%) / 17

⇒ wt % = (15.2 × 17) / (10 × 0.898)

⇒ wt % = 28.775 %

- Let the mass of solution of x be 100 gm

⇒ Mass of x = 28.775 gm

& Mass of water = 71.225 gm

- Mole fraction of x = (28.775/17) / {(28.775/17) + (71.225/18)}

⇒ X = 1.693 / {1.693 + 3.957}

⇒ X = 1.693 / 5.65

⇒ X = 0.2996 ≈ 0.3 (approx)

- So the mole fraction of x is approximately 0.3 .

Answer 2

Given:

Density of a solution = 0.898 g/ml

Molar mass of a solution = 17 gm

Molarity of a solution = 15.2 m

To Find:

The mole fraction of x = ?

Solution:

As we know,

$Molarity=\frac{(10\times d\times wt \ percent)}{M.wt}$

On putting the values in the above formula, we get

$15.2=\frac{(10\times 0.898\times wt \ percent)}{17}$

$wt \ percent=\frac{(15.2\times 17)}{10\times0.898}$

$wt \ percent=28.775 \ percent$

∵ percent = %

Now,

let the mass of the solution of "x" be "100 gm"

Mass of x = 28.775 %

Mass of water = 71.225 gm

$Mole \ fraction \ of \ x =(\frac{28.775}{17})/(\frac{28.775}{17})+(\frac{71.225}{18})$

$X=\frac{1.693}{1.693+3.957}$

$X=\frac{1.693}{5.65}$

$X=0.2996$

$X=0.3 \ (approx)$

Thus, the mole fraction of x will be "0.3".